“Libyan Raids Show Obama Doctrine in Action,” read a Wall Street Journal headline this week. “Sussing Out An Emerging Obama Doctrine,” said another headline from NPR. According to this reading, Obama is willing to use force to prevent a humanitarian catastrophe but only if it involves a real multilateral coalition in accordance with international law, which stands in stark contrast to the Bush Doctrine of unilateral, pre-emptive war.

Yet an increasing number of prominent pundits and politicians believe Obama has failed to articulate the very sort of doctrine that should supposedly guide him through an international crisis like Libya. “I don’t think there is an Obama doctrine,” Newt Gingrich said this week. (One shudders to imagine what a Gingrich doctrine would entail.) “What I think is needed right now is what I would call an Obama doctrine, which lays out a framework for intervention or nonintervention,” added former Colorado Senator Gary Hart (whose views on foreign policy are much more cogent than Gingrich’s).

But would a fixed Obama doctrine, of the sort that Bush had, have really helped Obama in Libya and the broader Arab world? The answer is no. I agree with Andrew Sullivan (a skeptic of the Libya intervention), who argued yesterday that “the US is navigating the currents of Middle Eastern history in a way that cannot be reduced to a doctrine.” The uprisings in the Arab world are too complex to be reduced to a one-size-fits-all doctrine.

The use of American force would have been inappropriate and counterproductive in Egypt and Tunisia. It’s not a reasonable option in Bahrain, which currently has a thousand Saudi troops stationed there. We don’t know who to trust in Yemen, and whether the fall of that country’s government would be a good thing for US national security interests. The same could be said about Libya, although if the international community had not stepped in, it’s very likely there would have been a bloodbath in Benghazi, which White House adviser Dennis Ross labeled “Srebrenica on steroids.” Good luck articulating a coherent doctrine that weaves together all these disparate elements and moving parts.

That’s not to say that Obama was right to intervene in Libya or should be immune from criticism—his administration did not adequately consult with Congress, has not laid out a clear endgame for the military mission and has not explained what a post-Qaddafi Libya would look like and whether that would actually benefit the United States. But let’s not pretend that an Obama doctrine would have rectified this situation or answered those questions.

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